If you have an Uno and you don't mind dedicating it to your wireless project, go with a shield. I have pulled my hair out troublshooting software crashes that turned out to be related to flakey connections (mostly power and ground) between my Uno and my prototyping board. Any little movement or vibration is likely to cause the CC3000 to go into some state that you can't recover from except with a reset. I have not seen this kind of problem using a Micro and breakout board on the same prototyping board probably because there's less relative movement between the CC3000 and everything else.
There are no differences between the breakout board and the shield except for the presence of the micro SD socket, which you can ignore if you don't need it. You don't need to adjust any code to account for the differences between the shield and the breakout board if you use the pins called out in the sketches for VBEN, CS and IRQ for the breakout board and you wire the breakout board correctly.